Dimensional Scaling

Loeser, J. G.; Herschbach, D. R.

doi:10.1007/978-94-009-0227-5_1

Cited by 5 publications

(1 citation statement)

References 78 publications

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“…In refs and , the authors introduces a dimensional interpolation formula with D = 0 and D = ∞ and calculate asymmetry (similar to asphericity), which is defined as …”

Section: Asphericitymentioning

confidence: 99%

Dimensional Interpolation for Random Walk

2021

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We employ a simple and accurate dimensional interpolation formula for the shapes of random walks at D = 3 and D = 2 based on the analytically known solutions at both limits D = ∞ and D = 1. The results obtained for the radius of gyration of an arbitrary shaped object have about 2% error compared with accurate numerical results at D = 3 and D = 2. We also calculated the asphericity for a three-dimensional random walk using the dimensional interpolation formula. The results agree very well with the numerically simulated results. The method is general and can be used to estimate other properties of random walks.

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“…In refs and , the authors introduces a dimensional interpolation formula with D = 0 and D = ∞ and calculate asymmetry (similar to asphericity), which is defined as …”

Section: Asphericitymentioning

confidence: 99%

Dimensional Interpolation for Random Walk

2021

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Semiclassical self-consistent field perturbation theory for the hydrogen atom in a magnetic field

Sergeev

Goodson

1998

Int. J. Quant. Chem.

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ABSTRACT:A recently developed perturbation theory for solving self-consistent field equations is applied to the hydrogen atom in a strong magnetic field. This system has been extensively studied using other methods and is therefore a good test case for the new method. The perturbation theory yields summable large-order expansions. The accuracy of the self-consistent field approximation varies according to field strength and quantum state but is often higher than the accuracy from adiabatic approximations. A new derivation is presented for the asymptotic adiabatic approximation, the most useful of the adiabatic approaches. This derivation uses semiclassical perturbation theory without invoking an adiabatic hypothesis.

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Bohr model and dimensional scaling analysis of atoms and molecules

Svidzinsky

Chen

Chin

et al. 2008

International Reviews in Physical Chemistry

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It is generally believed that the old quantum theory, as presented by Niels Bohr in 1913, fails when applied to few electron systems, such as the H 2 molecule. Here we review recent developments of the Bohr model that connect it with dimensional scaling procedures adapted from quantum chromodynamics. This approach treats electrons as point particles whose positions are determined by optimizing an algebraic energy function derived from the large-dimension limit of the Schro¨dinger equation. The calculations required are simple yet yield useful accuracy for molecular potential curves and bring out appealing heuristic aspects. We first examine the ground electronic states of H 2 , HeH, He 2 , LiH, BeH and Li 2 . Even a rudimentary Bohr model, employing interpolation between large and small internuclear distances, gives good agreement with potential curves obtained from conventional quantum mechanics. An amended Bohr version, augmented by constraints derived from Heitler-London or Hund-Mulliken results, dispenses with interpolation and gives substantial improvement for H 2 and H 3 . The relation to D-scaling is emphasized. A key factor is the angular dependence of the Jacobian volume element, which competes with interelectron repulsion. Another version, incorporating principal quantum numbers in the D-scaling transformation, extends the Bohr model to excited S states of multielectron atoms. We also discuss kindred Bohr-style applications of D-scaling to the H atom subjected to superstrong magnetic fields or to atomic anions subjected to high frequency, superintense laser fields. In conclusion, we note correspondences to the prequantum bonding models of Lewis and Langmuir and to the later resonance theory of Pauling, and discuss prospects for joining D-scaling with other methods to extend its utility and scope.

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Dimensional Scaling

Cited by 5 publications

References 78 publications

Dimensional Interpolation for Random Walk

Dimensional Interpolation for Random Walk

Semiclassical self-consistent field perturbation theory for the hydrogen atom in a magnetic field

Bohr model and dimensional scaling analysis of atoms and molecules

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